Abstract
Interval computations estimate the uncertainty of the result of data processing in situations in which we only know the upper bounds Δ on the measurement errors. In interval computations, at each intermediate stage of the computation, we have intervals of possible values of the corresponding quantities. As a result, we often have bounds with excess width. In this paper, we show that one way to remedy this problem is to extend interval technique to rough-set computations, where at each stage, in addition to intervals of possible values of the quantities, we also keep rough sets representing possible values of pairs (triples, etc.).
The paper’s outline is as follows: we formulate the main problem (Section 1), briefly overview interval computations techniques solve this problem (Section 2), and then explain how the main ideas behind interval computation techniques can be extended to computations with rough sets (Section 3).
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References
Ceberio, C., Ferson, S., Kreinovich, V., Chopra, S., Xiang, G., Murguia, A., Santillan, J.: How to take into account dependence between the inputs: from interval computations to constraint-related set computations. In: Proc. 2nd Int’l Workshop on Reliable Engineering Computing, Savannah, Georgia, February 22-24, pp. 127–154 (2006); final version: Journal of Uncertain Systems 1(1), 11–34 (2007)
Ferson, S.: RAMAS Risk Calc 4.0. CRC Press, Boca Raton (2002)
Ferson, S., Ginzburg, L., Kreinovich, V., Aviles, M.: Computing variance for interval data is NP-hard. ACM SIGACT News 33(2), 108–118 (2002)
Jaulin, L., Kieffer, M., Didrit, O., Walter, E.: Applied Interval Analysis. Springer, London (2001)
Klir, G., Yuan, B.: Fuzzy Sets and Fuzzy Logic. Prentice Hall, Upper Saddle River (1995)
Kreinovich, V., Lakeyev, A., Rohn, J., Kahl, P.: Computational Complexity and Feasibility of Data Processing and Interval Computations. Kluwer, Dordrecht (1997)
Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning About Data. Kluwer, Dordrecht (1991)
Shary, S.P.: Solving tied interval linear systems. Siberian Journal of Numerical Mathematics 7(4), 363–376 (2004) (in russian)
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Kreinovich, V. (2011). Towards Faster Estimation of Statistics and ODEs Under Interval, P-Box, and Fuzzy Uncertainty: From Interval Computations to Rough Set-Related Computations. In: Kuznetsov, S.O., Ślęzak, D., Hepting, D.H., Mirkin, B.G. (eds) Rough Sets, Fuzzy Sets, Data Mining and Granular Computing. RSFDGrC 2011. Lecture Notes in Computer Science(), vol 6743. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21881-1_2
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DOI: https://doi.org/10.1007/978-3-642-21881-1_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21880-4
Online ISBN: 978-3-642-21881-1
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